Many studies suggest that there is a link between exercise and healthy bones. Ex

Question

Many studies suggest that there is a link between exercise and healthy bones. Exercise stresses bones and causes them to get stronger. One study examined the effect of jumping on the bone densities of 30 growing rats. There were three jump conditions: a control with no jumping, a low-jump condition (the jump height was 30 cm) and a high-jump condition (60 cm). After 8 weeks of 10 jumps per day, 5 days a week, the bone density (in mg/cm2) was measured.
(a) In designing this study, explain why the rats should be randomized to one of the three different jump conditions.
(b) Suppose there are 15 male rats and 15 female rats available in the experiment. What is a block in an experiment? Explain why gender could be used as a block in this experiment.

Explanation / Answer

(a) In a completely randomized design, experimental units are randomly assigned to treatment conditions.With a randomized block design, the experimenter divides participants into subgroups called blocks, such that the variability within blocks is less than the variability between blocks. Then, participants within each block are randomly assigned to treatment conditions. Because this design reduces variability and potential confounding, it produces a better estimate of treatment effects

(b)Blocking reduces variability. Its principle lies in the fact that a variability that cannot be overcome (e.g. needing two batches of raw material to produce 1 container of a chemical) is confounded or aliased with a(n) (higher/highest order) interaction to eliminate its influence on the end product. High order interactions are usually of the least importance (think of the fact that temperature of a reactor or the batch of raw materials is more important than the combination of the two - this is especially true when more (3, 4, ...) factors are present) thus it is preferable to confound this variability with the higher interaction.The sex of the rats is a blocking factor accounting for treatment variability between males and females. This reduces sources of variability and thus leads to greater precision.

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